In wireless communications, a communication channel includes channel coefficients such as gain and phase factors as well as noise factors. For the one-tap linear model, we assume that the channel coefficients and the noise signal are given as and , respectively. Then, the received signal at the receiver is represented as
where is the transmission signal at the transmitter and is the transmission power.
Rayleigh Fading ChannelEdit
When a fading model of given wireless channel can be represented as Rayleigh distribution, we model both the complex channel coefficient and the noise signal are normalized Gaussian random variable, i.e., distributed with .